Resonant probe driving arrangement and a scanning probe microscope including such an arrangement

ABSTRACT

A drive system is provided for a resonating probe device, such as a scanning probe microscope, wherein the amplitude of the drive signal is controlled by feeding back a phase shifted and amplified component of the amplitude of oscillation of the resonating element. Means are provided for electronically enhancing the quality factor of a resonating probe device when operated in a liquid environment. Such enhancement of the quality factor improves the sensitivity of the probe device.

The present invention relates to an apparatus for, and method of drivinga mechanical oscillator as, for example, found in scanning probemicroscopes or in chemical sensors and bio-sensors utilising resonatingstructures. The use of positive feedback makes it possible to modify theperformance of the oscillator, especially within a liquid environment.

Scanning force microscopy, which includes atomic force microscopy (AFM)uses a microscopic cantilever to provide atomic and molecular resolutionof organic and inorganic substances in air, ultra high vacuum, and inliquids. The cantilevered element is formed with a sharp tip on amicroscopic scale. If the tip of the cantilever is brought into closeproximity with the surface of a sample or medium under investigation,forces on the atomic scale cause an interaction between the very endmost section of the tip, and typically a single atom thereon, and anatom or molecule in the sample. This interaction can be measured, andused for imaging surfaces on the nanometer scale, or for measuringmechanical properties of the sample, or adhesion between the sample andthe tip.

Some of the main limitations to achieving high resolution have been themechanical properties of the sample and the adhesion between the sampleand the substrate. The issue of adhesion has been particularly criticalin materials such as biomolecules. The native structure of biomoleculesis best imaged in a buffer solution. However, in these conditions thebiomolecules exhibit low adhesion on atomically flat substrates such asmica or graphite due to the screening of attractive forces. The tip ofthe microscopic sensor is scanned with respect to the surface of themedia under investigation, for example in a raster scanning form, inorder to produce an image of a portion of the media. This scanningmotion can give rise to lateral forces that appear at the tip of thesensor during the scan which, in a traditional contact mode of scanningcan displace or destroy the molecules under investigation. Furthermore,researchers have reported that the visualisation of undistortedbiomolecules at molecular resolution requires forces as small as 100 pNto be resolved.

Scanning force microscopes can be operated in a dynamic or intermittentcontact mode in which the cantilever oscillates by a few manometers, andmay intermittently touch the sample. This technique has significantlyreduced the lateral forces, allowing routine imaging of proteins, DNAand cells. However the forces acting along the surface normal are stillof the order of several nano newtons, thereby preventing highresolution.

The force required to excite a cantilever to a given amplitude A is kA/Qwhere k is the spring constant of the cantilever and Q is the qualityfactor. This expression is valid if the excitation frequency is equal tothe resonance frequency of the cantilever and thereby gives anindication of the force applied to the sample. However this expressionalso indicates the main limitation of oscillating the cantileveredelement in a liquid, namely the low quality factor of the cantilever ina liquid environment.

A further complication arises from the driving mechanism used in theliquid environment. The cantilever is usually excited through acousticwaves induced in the liquid by a piezoelectric element placed in theliquid. This allows coupling to occur at frequencies where the liquidresonance is coupled to the cantilever resonance, this coupling can, asshown in FIG. 1 of the accompanying drawings, make it exceptionallydifficult to identify the resonance peak of the cantilever. The realfrequency spectrum of the cantilever can be seen by directly excitingthe cantilever. For the purposes of identifying the resonance spectrumof the cantilever, the cantilever was coated with a thin layer offerromagnetic material and excited by applying a sinusoidal magneticforce in the vicinity of the cantilever. A comparison of FIGS. 1 and 2shows that the spectrum obtained by mechanical excitation has many peakscompared to the cantilever's resonance spectrum, and also that theresonance peak of the cantilever is broad. In fact, the stronghydrodynamic force between the cantilever and the fluid surrounding itresults in very low quality factors, in the region of about 1 to 4 beingobtained which is approximately two orders of magnitude lower than thosethat would be expected for operating a similar cantilever in air. Thislimits the minimum force applied to the sample, and thus for the usualconditions which might be expected in a tapping mode of operation k=0.4Nm⁻¹, Q=2 and A=5 nm, the excitation force is about 1 nN. Thisexcitation force is about two orders of magnitude higher than the forcessuitable for the visualisation of the stricture of biomolecules at amolecular level.

It is also known that chemical and bio-sensors utilisingmicro-fabricated cantilevers of silicon or silicon nitride can be madeby coating one or both sides of the cantilever with a suitable reagentor receptor. Where both sides of the cantilever ate coated with areceptor (i.e. sensing molecules) the effective mass of the cantileverchanges in the presence of the appropriate receptor-binding ligand (i.e.molecules to which the sensing molecules are sensitive). A surfacestress method may also be employed in which only one side of thecantilever is coated with a receptor. The surface stress on this side ofthe cantilever changes as the target substance interacts with thereceptor, producing a cantilever bending as the surface expands orcontracts. The motion of the cantilever can be optically examined, forexample to look for bending of the cantilever by using an optical leverto magnify the deflection from the cantilever. The reflected light canbe detected by a pair of photo-detectors and the position of thecantilever can be established by looking at the ratio of the outputsfrom the photo-detectors.

Bio-sensors and chemical sensors for use in liquids have hitherto beenfabricated using the surface stress method because the surface energy(and hence tendency for the cantilever to bend) is very sensitive to theadsorption of a sub-monolayer of material, whilst the correspondingchange in mass can be negligible. The micro-fabricated cantilever areextremely sensitive to temperature, and initial drift resulting fromtemperature fluctuations and chemical reactions with the cantilever canbe significant. In fact Butt (J colloid and interface Sci, 180 (1996)251) has reported experiments with chemical sensors and bio-sensors inliquid using the surface stress method in which the apparatus needed toequilibrate for 1 to 2 days before measurement could be taken.

Scanning probe microscopes are commercially available. Workers haveinvestigated schemes for modifying the effective Q of the sensor tip. BAnczykowski et al. “Analysis of the interaction mechanisms in dynamicmode SFM by means of experimental data and computer simulation” AppliedPhysics A 66, 5885-5889 (1998) describe using a feedback mechanism tovary the effective Q of a nanosensor which should work well in a vacuumor low loss environment.

A set up for modifying the effective Q of a sensor is illustrated inFIG. 3. A laser 1 is used to illuminate a cantilever 2. The cantilever 2is driven by a piezoelectric element which receives a drive signal froma function generator 4 via an adder 5. Light reflected from thecantilever is directed by an optical path 6 towards a processor 10 forforming the ratio of, or the difference between the signals, received ata pair of photo-detectors. Other detectors of the cantileveroscillation, such as a tuning fork, optical interference etc. could beused.

As shown, a portion of the received signal from the detection circuit 10is fed to a variable phase shifter 12, and from the phase shifter to avariable gain amplifier 14. The output of the amplifier is then added tothe signal supplied from a function generator 4 and used to drive thesensor via the piezoelectric element.

This system should work well in a vacuum or low loss environment.However in a liquid environment the operating properties of thecantilever can change as it comes into proximity with the surface underinvestigation, consequently the feedback system will supply a drivesignal which is not at the resonant frequency of the probe. Furthermorebecause the coupling between the probe and the driver in a fluid filledsystem need not be that strong, this can result in instances where thefeedback signal from the probe is at a different frequency to the drivesignal, thereby giving rise to interference at the drive frequency whichmay manifest itself as a beat which amplitude modulates the drive signalthis in turn degrades the signal measurement capabilities of themicroscope. Additionally, because of the low quality factor in liquid,energy is distributed into the higher harmonics of the cantilever. Thesehigher harmonics may have a different experimental phase response to thefirst harmonic, and when their higher frequency amplitude signal is fedback into the drive signal, it will tend to destabilise the motion ofthe cantilever.

Other prior art arrangements are known. U.S. Pat. No. 5,966,053discloses an apparatus for controlling a mechanical oscillator. Afeedback signal from the mechanical oscillator is mixed with a referencefrequency in order to frequency convert it to an intermediate frequency.The intermediate signal is provided to a phase locked loop and to afirst input of a balancing network. A second input of the balancingnetwork receives an output of the phase locked loop. The balancingnetwork combines the signals at its inputs, these are then phase shiftedand amplified. The phase shift is provided to ensure that an appropriatephase relationship can be maintained between the driving signal asgenerated by the feedback loop and cantilever's response. The gain iscontrolled to ensure that the output of the amplifier is set to apredetermined value before the signal is frequency converted to thecantilever's resonant frequency.

In a fluid environment as the end of the cantilever approaches thesurface of the sample sufficiently closely (in the order of 1 μm), thefluid medium surrounding the cantilever can effectively become trappedbetween the cantilever and the sample under investigation. This can giverise to both a change in the effective mass of the resonating cantileverand the spring constant. These effects do not occur when equivalentscanning force microscopy is carried out in a gaseous or high vacuumenvironment, and consequently workers in this field have ignored theseeffects.

In order to implement scanning force microscopy in a liquid environment,it is desirable to be able to measure the resonant frequency of thecantilever, to track the resonant frequency accurately, and tosynthesise a higher quality factor.

For bio-sensor and chemical sensor work the issue of fluid trappingadjacent the cantilever, or such other resonant structure as may befabricated, may also be an issue if the cantilever is fabricated closeto a substrate.

According to a first aspect of the present invention, there is provideda control apparatus for controlling a driving signal used to stimulate aresonating sensing element, in which the control apparatus is responsiveto a sensor used to monitor the motion of the sensing element and inwhich the control apparatus comprises a signal processor for filteringsignals from the sensor so as to remove harmonics above a predeterminedorder from the signal, and a drive signal controller responsive to theoutput of the signal processor for adjusting the driving signal so as tomaintain the sensing element in resonance.

The signal processor may be a digital or analogue device and may performone or more of filtering, phase locking, phase shifting or other signalprocessing operations.

Preferably the sensing element is a micro-fabricated element. Such anelement may be a resonant bridge, but preferably is a cantilever.Preferably the cantilever is part of a scanning force microscope. Thecantilever may be arranged such that its longitudinal axis issubstantially parallel to a nominally flat surface under investigation.Alternatively the cantilever may be arranged such that its longitudinalaxis is substantially normal to a planar surface under investigation.Both these modes of operation can be used to investigate the propertiesof the surface. Similarly both these configurations may be used inchemical sensors, bio-sensors or other sensors where the response of theelement can be modified by an external influence.

The sensing element is preferably driven by a piezoelectric element oran alternating magnetic or an alternating electrostatic field, or by anyother means.

Alternatively a drive element may be mechanically coupled to the sensingelement via a liquid medium.

Preferably the sensor for monitoring the motion of the sensing elementis an optical sensor. Commercially available scanning force microscopesalready often include optical detection of the motion of the sensingelement and hence existing detection technology can be used. Othersensing technologies may be used, such as piezo-resistive elements.

Preferably the control apparatus analyses the signal from the sensor toidentify a phase shift between the motion of the sensing element and thedriving stimulus applied to the element.

Preferably the drive signal controller adjusts the phase of the drivingsignal so as to maintain the phase shift at substantially apredetermined value.

Preferably the phase shin is maintained at 90 degrees, thereby ensuringthat the sensing element is driven at its resonant frequency. However,the other phase shifts could be maintained if desired.

Preferably the phase shift is measured by a phase sensitive detector,such as a lock-in amplifier. However it will be appreciated that digitalprocessors and the like may also be used to measure the phasedifference. Advantageously the output of the phase detector is fed to acontrol input of the voltage control oscillator via a controller, suchas a proportional-integral controller which serves to cause the phasedifference to tend towards its predetermined value.

Advantageously at least one further feedback loop is provided forcontrolling a property, such as the amplitude, of the drive signalsupplied to the sensing element. This may be performed by amplifying andfeeding a phase shifted detector signal back to the driver.Alternatively, the amplitude of the frequency generator may be directlymodulated as a function of the detector signal in order to control theamplitude of the drive signal. Advantageously the detector signal isfiltered to reduce the higher frequency content of the signal. That is,to prevent the signal from the higher harmonics from being fed back intothe drive signal. This feedback loop performs a positive feed backsystem thereby simulating an effective Q in excess of the actual Q ofthe sensor.

Additionally or alternatively a single parameter of the detector signalmay be measured and used to control a parameter of the drive signal. Asinusoid can be considered as having three parameters that define it,namely frequency, amplitude and phase. For systems which take the sensorsignal, amplify it and add it to the drive signal, it follows that theamplitude, phase and possibly frequency spectrum of the drive signal aremodified as a result of the feedback from the drive signal. However, ifonly the phase of the sensor signal was measured (discarding the othertwo parameters) then this single parameter could be used to control asingle parameter of the drive signal, for example it's phase. Thisconcept could be extended to cover two of the parameters while omittingthe third.

According to a second aspect of the present invention, there is providedan apparatus for controlling the amplitude of a drive signal applied toa resonating sensing element, the controller being responsive to atleast one sensor for measuring the oscillation of the sensing element,and comprising a signal processor for extracting a parameter of theoscillation, and for using the parameter of oscillation to control aparameter of the power supplied to drive the sensing element inaccordance with a first transfer function, and at least one of thesignal processor and the drive element being unresponsive to otherparameters of the oscillation.

Preferably the parameter of oscillation is the magnitude of theoscillation and only information about the magnitude is used to controlthe signal sent to the drive element for driving the sensing element.Additionally or alternatively only the phase or only the frequency ismeasured and used to control the phase or frequency, respectively, ofthe drive signal. Thus, in essence, the multiple parameters used todefine the sinusoid are made orthogonal to one another and the feedbackloop only sees (and passes information pertaining to) it's associatedone of the parameters. Multiple feedback loops may be provided to handlethe parameters independently of each other.

According to a third aspect of the present invention, there is providedan apparatus for driving a resonating element at its resonant frequency,the apparatus comprising a frequency signal generator for generating adrive signal and drive means responsive to the drive signal so as toexcite the resonating element, at least one detector for detecting aresponse of the resonating element to the drive signal and signalprocessing means for measuring a phase shift between the drive signaland the response thereto and for controlling the frequency of the drivesignal so as to maintain a predetermined phase shift.

According to a further aspect of the present invention, there isprovided a method of driving a resonating element, comprising the stepsof monitoring the vibratory motion of the resonating element, comparinga phase difference between a signal used to excite the resonatingelement and the motion of the element, and varying the frequency of thesignal used to excite the resonating element so as to maintain the phasedifference at a predetermined value.

Embodiments of chemical, bio-chemical or other sensors utilisingresonating structures and constituting aspects of the present inventionmay comprise arrays of resonating elements. Thus, for example, aplurality of micro-machined cantilevers may be provided in an array.Each cantilever may be sensitised to detect different targets, chemicalsor reagents. Additionally and/or alternatively, a few cantilevers may beused to act as references to isolate non-specific signals. Thecantilevers may be fabricated to have distinct and different resonantfrequencies. In such an arrangement a single transducer and detector maybe used to drive and interrogate all of the transducers eithersimultaneously or in sequence. Since each transducer resonates at anindividual frequency, a drive signal to resonate all of the transducerscan be constructed as the superposition of the individual resonatingfrequencies. Similarly, the signal received from the detector elementwill also be a superposition of the motions of the individualcantilevers. These individual signals can be separated from one another,for example by filtering in either the analogue or digital domains, andthen acted upon by individual controllers, again in either the analogueor digital domains. Alternatively, a single frequency stepablecontroller may be arranged to access each cantilever in turn.

Additionally and/or alternatively where multiple resonating elements areprovided they may be coupled together, either by direct connection orthrough mechanical transfer within the fluid in order that a test forthe presence, absence or a mixture thereof of multiple reagents/targetsmay be detected via a single drive and interrogation process.

Typically a cantilever is fabricated over a pit formed in the silicon ora silicon nitride substrate. Either one or both of the cantilever andpit may be coated with one or more receptor substances. Thus it ispossible that the pit or silicon substrate may be treated with a firstsubstance which reacts with target compound to form a by-product, andwherein the sensing element may be coated with a substance responsive tothe by-product. Thus direct detection of target substances may beperformed.

The present invention will further be described, by way of example, withreference to the accompanying drawings, in which:

FIG. 1 is the spectrum of a v shaped cantilever (k=0.58 Nm⁻¹) excited bymechanic-acoustic excitation of a fluid;

FIG. 2 is the excitation spectrum of the cantilever of FIG. 1 in afluid, but excited using a magnetic field;

FIG. 3 schematically illustrates the sensing and feedback arrangement ofa prior art scanning force microscope;

FIG. 4 is a schematic diagram illustrating the components constitutingan embodiment of the present invention;

FIG. 5 is a block diagram of a first embodiment of the presentinvention;

FIG. 6 is a block diagram of a second embodiment of the presentinvention;

FIG. 7 is a block diagram of a third embodiment of the presentinvention;

FIG. 8 is a block diagram of a fourth embodiment of the presentintention.

FIG. 9 illustrates the response of the cantilever to the drive signal asa function of frequency in a mechanical excitement mode, when Qenhancement is applied;

FIG. 10 represents the response of the cantilever as a function offrequency with Q enhancement when driven by magnetic field excitation;

FIGS. 11 a-11 d schematically compare experimental results of topographprofiles (FIGS. 11 a and 11 b) and corresponding phase response (FIGS.11 c and 11 d), where FIGS. 11 a and 11 c are taken without Qenhancement and FIGS. 11 b and 11 d were measured using Q enhancement.

FIG. 12 illustrates results obtained using a scanning force microscopewith Q enhancement to examine the dynamic properties of molecules;

FIG. 13 illustrates a control apparatus constituting a furtherembodiment of the present invention;

FIG. 14 schematically illustrates a chemical sensor constituting anembodiment of the present invention;

FIGS. 15 a and 15 b illustrate experimental results illustratingvariations in deflection and resonant frequency, respectively, for acantilever as a result of thermal drift;

FIGS. 16 a and 16 b illustrate experimental results showing changes inresonant frequency for a chemical sensor constituting an embodiment ofthe present invention, and

FIGS. 17 a and 17 b illustrate changes in deflection and resonantfrequency for a micro-machined cantilever.

For an oscillating cantilever the excitation force applied thereto iscomposed of the sum of two signals. One of these signals is thesinusoidal excitation force F₁−F₀e^(jωt), and the other is the feedbacksignal derived from the motion sensor, typically a photo diode, that isamplified and phase shifted.

The cantilever oscillation in intermittent contact with the sample canbe expressed as:Z=Z _(o) +A ₁ e ^(j(ωt−φ)) +A ₂ e ^(j)(2ωt−φt)+Ideally, if the feedback loop is working correctly, the second term ofthe excitation force applied to the cantilever is given by:F ₂ =GA ₁ e ^(j(ωt−φ+π/2))Neglecting minor contributions of higher order harmonics, this force isproportional to the velocity of the cantilever:$\frac{\mathbb{d}z}{\mathbb{d}t} = {\omega\quad A_{1}{\mathbb{e}}^{j{({{\omega\quad i} - \phi + \frac{\pi}{2}})}}}$Then the differential equational that governs the motion of thecantilever can be approximated by:${{m\quad\frac{\mathbb{d}^{2}Z}{\mathbb{d}t^{2}}} + {\left( {\gamma - {G/\omega}} \right)\frac{\mathbb{d}z}{\mathbb{d}t}} + {K\quad Z} - F_{int}} = {F_{o}{\mathbb{e}}^{j\quad\omega\quad t}}$

-   -   Where F_(int) is the interaction force between the tip and the        sample,    -   Z is the vertical displacement    -   γ is the damping coefficient and    -   ω represents angular frequency.

In other words, the cantilever oscillates with an effectivedamping/viscosity that can be electronically tuned.

FIG. 4 schematically illustrates a control system for use with ascanning force microscope. The scanning force microscope has a sensorhead 20 which comprises a transducer 22, such as a piezo electric deviceand a sensor element 24, which typically (though not exclusively) is aphoto diode for detecting motion of the cantilever 23. These elementsare commercially available and need not be described further here. Aamplitude and/or phase feed back unit 26 is arranged to be responsive tothe sensor 24 and to modify the driving signal to the transducer 20.However, unlike the prior art system shown in FIG. 3 this control systemalso includes a frequency tracking element 28 which can modify the drivefrequency applied to the transducer in order to follow changes in theresonant frequency of the cantilever, and a filter to filter theamplitude response of the cantilever at frequencies corresponding to thehigher harmonics of the cantilever.

As shown in FIG. 5, a first embodiment of the present invention combinesthe feedback and frequency tracking electronics 26 and 28 within asignal processing unit 30. A voltage controlled oscillator 32 has anoutput connected to a first input of a summer 34 and also to a referenceinput (ref) of a phase detector 36. An output of the summer 34 isprovided to a transducer 22 constituting part of the microscope scanninghead. An output of the position sensor 24 is provided to an input of alow pass filter 70 and also to a signal input (sig) of the phasedetector 36. An output of the filter 70 is provided as an input of avariable phase shifter 37. An output of the phase detector 36 isprovided to an input of a controller 38 such as a proportional-integral(PI) controller which has an output connected to a control input of thevoltage controlled oscillator 32. An output of the variable phaseshifter 37 is provided to an input of a variable gain amplifier 40. Anoutput of a variable gain amplifier 40 is provided to a second summinginput of the summer 34. An output of the sensor 24 is also provided asan output 42 which may be connected (optionally via buffering) to dataacquisition apparatus.

The phase detector 36, PI controller 38 and voltage controlledoscillator 32 form a frequency phase locked loop controlling the drivesignal. The action of the phase detector 36 and PI controller 38 isselected to vary the output frequency of the voltage controlledoscillator in order to maintain a predetermined phase difference betweenthe signals occurring at the reference input and signal input of thephase detector 36. By setting this predetermined phase difference to be90°, it is possible to ensure that the voltage controlled oscillatoralways drives the cantilever of the microscope at its resonantfrequency. This resonance condition is maintained in a feedback loopsuch that this condition is always satisfied even though the resonantfrequency of the cantilever itself may change during operation in afluid environment. Other predetermined phase differences can bemaintained if desired for operation away from resonance, for example onthe steep sided section of the resonance curve.

The variable phase shifter 37 and variable gain amplifier 40 serve toform a positive feedback loop optimising the characteristics of thecantilever, such as its Q factor. The variable phase shifter is includedto compensate for any phase shift occurring in the amplifier and/or lowpass filter such that the output of the amplifier can remain in phasewith the output of the voltage controlled oscillator. Thus positivefeedback is provided which serves to further enhance oscillations of arelatively large intensity by increasing the mechanical drive applied tothe transducer. By controlling the transfer function of the variablegain amplifier, it becomes possible to synthesise a higher Q factor forthe oscillating cantilever than that which it actually possesses. Somemodification of the positive feedback system may be provided tostabilise the amplitude of the cantilever oscillation so as to ensureit's response does not become unpredictable or unrepeatable, and thatdamage does not occur.

FIG. 6 shows a further embodiment, in which like parts are representedby like reference numerals. This arrangement does not include the phaselocked loop in the previous embodiment, but is otherwise the same. Asinusoidal signal, for instance from a signal generator, provides thefirst input 43 of the summer 34. Because of the presence of the filter70, positive feedback is provided without the destabilising presence ofthe higher harmonics in the feedback signal. The phase lock loop can beomitted providing the resonant frequency is not substantially changed byapproaching the surface, for example if the drive frequency is selectedclose to the surface.

FIG. 7 shows a further embodiment, in which like parts are representedby like reference numerals. In this arrangement the output of thevoltage controlled oscillator is provided to a first input of a voltagecontrolled variable gain amplifier 50 whose output is connected to thetransducer. An output of the sensor 24 is connected to a sensing inputof the phase detector 36, as described with reference to FIG. 5, butalso to an input of a rectifier 52. The output of the rectifier 52 isconnected to a gain control input of the variable gain amplifier. Asbefore, the phase detector 36, PI controller 38 and voltage controlledoscillator 32 form a frequency, feedback control loop. The rectifier 52detects the root mean square or peak value of the oscillation of thecantilever, and uses this to control the gain applied by the variablegain amplifier to the output of the voltage controlled oscillator. Thusas before, the magnitude of the drive signal applied to the transducer22 increases as the magnitude of oscillation of the cantileverincreases.

FIG. 8 shows a further alternative arrangement in which the phasedetector 36, PI controller 38 and voltage controlled oscillator 32 areconnected as described hereinbefore. However the output of the voltagecontrolled oscillator is provided to a input of a voltage controlledvariable phase shifter 62. An output of the phase shifter 62 is providedto the transducer 22. An output of the sensor 24 is provided to a firstinput of a second phase detector 60, a second input of which receives anoutput from the voltage controlled variable phase shifter. The phasedetector 60 forms a signal representative of the phase differencebetween its inputs, and the signal is used to control the phase shiftintroduced by the variable phase shifter 62. The positive feedback loopformed by phase detector 60 and phase shifter 62 has a significantlyshorter time constant than the phase locked loop. The positive feedbackloop increases the effective quality and reduces the error within thephase locked loop.

By way of comparison, FIG. 9 and FIG. 10 show the response of thecantilever when driven using a control circuit constituting anembodiment of the present invention. FIG. 9 shows the spectrum of thecantilever when excited through mechanic-acoustic waves, andconsequently compares directly with FIG. 1. FIG. 10 shows the resonantspectrum when the cantilever is excited via a magnetic field, andconsequently compares with FIG. 2. The magnetic excitation produces avery narrow resonance peak with an effective Q of approximately 280.Furthermore, this peak corresponds to the most dominant of those peakslocated when the cantilever is driven by mechanic-acoustic waves. Thehigh effective Q overcomes the low transmission of the excitation forcethrough the liquid at the natural frequency of the cantilever, andallows the identification of the resonance frequency without the need ofa direct excitation method in which a magnetic cantilever coating isrequired.

The sensitivity of the cantilever is proportional to Q, and effective Qfactors have been reached which are more than two orders of magnitudegreater than the natural Q of the cantilever in fluid. The Inventorshave checked the improved sensitivity by imaging a very soft sample of1% agoros gel. This sample had an elastic modulus of 150 kPa. FIGS. 11 aand 11 b show the topography and phase shift image of the sample with astandard silicon nitride tip having a normal spring constant of 0.37Nm⁻¹. The free and damped amplitudes are 6 and 5.5 nm respectively. Thesame region of the sample was imaged with the same tip using asynthesised Q for about 153. This produced a significant increase in thespatial resolution as a consequence of the lower force applied. Lowerforces imply lower indentations of the tip into the gel and thereforehigher resolution, as shown in FIG. 11 c. On the other hand, the phaseshift between the cantilever oscillation and the excitation signal ismore sensitive to topographic changes, as shown in FIG. 11 d.

The inclusion of electronic tuning of the quality factor increases thesensitivity of the microscope in an ordinary tapping mode in liquid.

An atomic force microscope having a resonating cantilever and qualityfactor control and frequency tracking control can be used to investigatethe properties of a single molecule. In essence, the resonatingcantilever can be brought into contact with a molecule and then thecantilever slowly raised above the surface of the sample so as tostretch the molecule. Where this has been done with non vibratingcantilevers, the result obtained is a force vs displacement curve.However, when an investigation is performed using a vibratingcantilever, it is also possible to estimate the conservative, elasticand dissipative forces. The dissipative forces can be examined bylooking at the change in amplitude of the resonance peak, whereas theelastic forces can be examined by virtue of the change in frequency.FIG. 12 shows the results obtained from investigating a molecule. Theabscissa represents the movement in the force sensing (stretching)direction. The curve labelled “A” represents the force gradient withrespect to changing distance. The curve labelled “B” represents thechange in amplitude, and hence is indicative of local dissipation, andthe curve “C” represents the total force experienced by the cantilever.It can be seen that contact between the tip and the sample fails atabout 120 nm on the X axis.

In a further embodiment of the present invention as shown in FIG. 13,the basic arrangement shown in FIG. 5 is modified by the inclusion of afurther feedback loop comprising a variable phase shifter 80 whichreceives a further input from the sensor 24, and a further variable gainamplifier 82 which receives an input from an output of the variablephase shifter 80. Also, the low pass filter 70 may be omitted, althoughbetter results may be obtained if it remains in the circuit. The outputof the variable gain amplifier 82 is summed with the output of thevoltage controlled oscillator 32. This further feedback loop is arrangedto shift the sensor signal through 0 or 180 deg in order to change theeffective spring constant, and thereby the resonant frequency.Optionally, the frequency tracking can be employed as hereinbeforedescribed, or it may be omitted.

Ideally the effect of this two feedback loops in the differentialequation of a oscillator is:Mz″+γz′+kz=F _(int) +F _(o) e ^(iωt) +G ₁ ze ^(iφ1) +G ₂ ze ^(iφ2)

Where M is the effective mass of the oscillator, γ is the dampingconstant, k is the spring constant, F_(int) is a possible interactionbetween the cantilever and the sample or environment and z representsthe oscillator motion. The excitation force is the sum of a sinusoidalexcitation force F_(o)e^(iωt), the sensor signal amplified and phaseshifted by the first feedback loop G₁ze^(iφ1), and the sensor signalamplified and phase shifted by the second feedback loop, G₁ze^(iφ2). Thesolution of this equation can be approximated by z=Ae^(i(ωtφ)).

For instance, if we fix φ1=90 deg and φ2=0 or 180 deg, the firstfeedback loop changes the effective damping constant by γ_(eff)=γ−G₁/ω,and the second feedback loop changes the effective spring constant byk_(eff)=±G₂.

The sensitivity with which the oscillation frequency can be detectedallows a resonating sensor to be used in other situations. For example aminiature sensor may be coated with a reagent such that, in the presenceof selected chemicals, a chemical reaction takes place.

The micro-cantilever is partially or totally surface treated with acompound selective substance having substantially exclusive affinity fora targeted compound in a liquid environment. The micro-cantilever sensoris also provided with one of the oscillation detection methods describedbefore. The frequency detection method is capable of detecting changesin the resonance frequency, amplitude or phase of the vibratedmicro-cantilever in the monitored liquid solution. Upon insertion into amonitored liquid solution, molecules of the targeted chemical attach tothe treated regions of the micro-cantilever resulting in a change inoscillating mass as well as a change in micro-cantilever spring constantor mechanical properties of the cantilever thereby influencing theparameters of the micro-cantilever oscillation. Furthermore, themolecular attachment of the target chemical to the treated regionsinduce areas of mechanical strain in the micro-cantilever consistentwith the treated regions thereby influencing micro-cantileveroscillation. The rate at which the treated micro-cantilever accumulatesthe target chemical is a function of the target chemical concentration.Consequently, the extent of micro-cantilever oscillation change(frequency, amplitude of phase) is related to the concentration oftarget chemical within the monitored liquid solution. Similarly, theequilibrium level of accumulated target chemical will depend on thetarget chemical concentration; consequently the extent ofmicro-cantilever oscillation change (frequency, amplitude or phase) isrelated to the concentration of target chemical within the monitoredliquid solution.

FIG. 14 schematically illustrates a chemical/bio-chemical sensorutilising a resonating cantilever. The drive arrangement is identical tothat shown in FIG. 5 of the accompanying drawings, except that this timethe resonating cantilever 100 is driven magnetically by a magnetic fieldgenerated by a coil 102 situated adjacent the cantilever. The magneticcoating on the cantilever 100 was produced by coating the cantileverwith chromium and then cobalt using thermal evaporation. A magneticmoment was produced in the thin film with a strongly orientated magneticfield.

In this experiment, the cantilever was sensitised to ethanol bydepositing a 2500 mm thick coating of poly-methyl-methacrylate (PMMA) onboth sides of the cantilever. However, antibodies may also beimmobilised on one side of the cantilever. The applicant has immobilisedthe antibody BRAC30 on one side of the cantilever in order to detect thepresence of the secondary antibody STAR71 which recognises an epitopelocated on the Fe fragment of BRAC30. In order to do this the originalgold coating on the cantilevers (which coating had been placed there bytheir manufacture) was removed by immersion in a mixture of hydrochloricand nitric acid. Then one side of the cantilever was coated with fivenanometers of chromium and 50 nanometers of gold using thermaldeposition. The gold coated cantilevers were immersed in one milimolarcystamine dihydroclhoride for 60 minutes and washed in two molar NaOHand miliQ water. The cantilevers were then immersed in glutoraldehyde(1%) for 60 minutes and rinsed in miliQ water. A droplet of the antibodyBRAC30 solution was deposited for 60 minutes. The glutoraldehyde acts asa covalent linker between the substrate and the antibody. The remainingaldehyde sites were then saturated by immersion of the cantilever for afew minutes in a suitable solution (bovine serum albumen solution).

This cantilever, as was found with the cantilevers for the scanningprobe microscope, exhibited a significant reduction in Q once thecantilever was immersed in liquid. In this instance, the resonantfrequency in air of the cantilever was approximately 50 kHz with aquality factor of approximately 70. Once the cantilever was immersed inliquid the resonant frequency reduced to approximately 16 kHz as aconsequence in the increase of effective mass of the cantilever as itdrags the surrounding liquid during oscillation. The quality factor alsoreduced to a value of approximately 2 due to hydrodynamic dampingbetween the cantilever and the liquid environment. However, by using thefeedback control circuit a synthesised quality of Q of approximately 625was obtained. Higher quality factors can be synthesised and theapplicant has achieved quality factors in excess of 1000 but theoscillation can become unstable for higher values as a consequence oflocal variations in the velocity of the liquid owing to thermalfluctuations.

The sensitivity of such a chemical sensor is approximately proportionalto its quality factor. A resonant frequency is detected by the phaselock loop and measures the phase shift between the cantileveroscillation and the driving signal, which phase difference is 90° atresonance. The phase shift deviation with respect to resonance isapproximately:ΔΦ=2Q(ω−ω₀)/ω₀for small ΔΦ. Thus higher Q factors allow smaller phase shifts to beresolved.

A significant feature of resonating cantilevers is that they aresubstantially insensitive to long term thermal drift which may show upin the DC response of a cantilever in liquid. FIG. 15 a demonstrates achange in cantilever deflection, which was measured at approximately 8nanometers per minute during an hour of operation, whereas thecorresponding resonant frequency was virtually unaffected, changing bysubstantially no more than 2 Hz over the time period.

The use of high value synthesised Q factors also enables the sensor tobe highly sensitive to the presence of a reagent. FIGS. 16 a and 16 bshow the results obtained from an experiment where a cantilever wascoated with a polymer layer of PMMA. FIG. 16 a shows the real timeresponse of the change in resonance frequency for exposure of thecantilever to 0.5% ethanol in water. The resulting response consists oftwo parts. Firstly, the resonant frequency drops suddenly by 50 Hz dueto the diffusion of the analyte into the polymer layer, therebyincreasing cantilever mass. Secondly, the resonant frequency increasesagain as the ethanol diffuses out of the polymer layer until it hascompletely evaporated. The applicant has calculated that the effectivemass increase resulting in the drop of resonant frequency amounted toapproximately 50 picogrammes.

The experiment was repeated, as shown in FIG. 16 b, with a solution of5% ethanol. In this experiment the resonant frequency decreased byapproximately 410 Hz. These data suggest that the sensitivity of thissensor is approximately 1% of ethanol per 100 Hz.

FIGS. 17 a and 17 b show the result of a similar experiment utilisingthe BRAC30 antibody in order to detect a target antibody, STAR71, in thepresence of the cantilever. The STAR71 target antibody binds thereceptor molecules attached on one side of the cantilever, therebychanging the surface energy of side of the cantilever with respect tothe other. The area of each side then contracts or expands in order tominimise the energy of the system, giving rise to cantilever beadingwhich corresponds to a deflection (Z) of:$z = {4\quad\frac{1 - v}{E\quad t^{2}}\quad L^{2}\left( {{\Delta\quad\sigma_{t}} - {\Delta\sigma}_{b)}} \right.}$

Where ν is poisson's coefficient, E is young's modulous, t is thecantilever thickness, L is length and Δσ_(t) and Δσ_(b) are the surfacestress changes on the top and bottom side of the cantileverrespectfully. By using E=96GP_(a) and ν=0.27 for silicon nitride, theestimated sensitivity is approximately 1.3 mJ/m² per nm of deflection.The surface stress produced results in a tension parallel to thecantilever surface that is proportional to the total surface stressΔσ_(t)+Δσ_(b). This tension contracts or expands the cantilever,changing the spring constant of the cantilever by:${\Delta\quad k} = {\frac{\pi^{2}n}{4n_{j}}\left( {{\Delta\quad\sigma_{t}} + {\Delta\sigma}_{b}} \right)}$where n is the ratio between the effective mass and total mass of thecantilever and n_(t) depends on cantilever geometry, being one for anideal spring.

FIGS. 17 a and 17 b illustrate an experiment showing the detection of abiological target. Initially, 5 μL of buffer solution were injected intoa measurement fluid cell. This resulted in an immediate change indeflection of the cantilever of approximately 7 nm ask illustrated inFIG. 17 a, whereas the resonant frequency remain unchanged. This changein deflection is attributed to a difference in temperature between thebuffer solution and the liquid in the fluid cell, which resulted indifferential thermal expansion of the gold layer on top of thecantilever and the silicon nitride forming the bottom of the cantilever.The resonant frequency of the cantilever is substantially immune to thisbi-material effect as the surface stress on one side of the cantileveris substantially balanced by an opposing surface stress on the otherside.

After approximately 700 seconds, 5 μL of the target substance wereinjected in order to reach a concentration of 0.8 μg per ml. Theresonant frequency immediately recorded a drop of 63 Hz. This indicatesthat the surface of the side of the cantilever on the which the receptormolecules were immobilized had decreased as a consequence of thesespecific binding of the target bio-molecule. The observed frequencychange corresponds to a decrease in surface energy of approximately 7 mJper m². However, in the deflection based measurement as shown in FIG. 17a, the temperature change resulting from the introduction of thissolution obscures the change in surface area thus prior art DC detectionmethods fail to register the introduction of the target bio-molecule,whereas the resonant frequency method does.

Multiple sensors may be fabricated in an array and coated with differentreagents. Each may then be addressed individually by time divisionfrequency multiplexing of the control apparatus to excite each resonatorin turn. Alternatively, multiple processing channels may be provided inparallel such that the resonators may be addressed concurrently.

In a further embodiment of the control system the phase shift and gainof an amplifier may be selected such that it naturally causes thecantilever to go into resonance. Thus self maintaining oscillations maybe established, and once these have, the gain of the amplifier can thenbe adjusted in a closed loop manner in order to hold the amplitude ofoscillation substantially constant.

It is thus possible to provide a sensitive, robust and inexpensivesensor.

1. A control apparatus for controlling a driving signal used tostimulate a resonating sensing element, in which the control apparatusis responsive to a sensor used to monitor the motion of the sensingelement characterized in that the control apparatus comprises a signalprocessor for filtering signals from the sensor so as to removeharmonics above a predetermined order from the signal, and drive signalcontroller responsive to the output of the signal processor foradjusting the driving signal so as to maintain the sensing element inresonance.
 2. A control apparatus as claimed in claim 1, characterizedin that said signal processor is further arranged to identify a phaseshift between the motion of the sensing element and the driving stimulusapplied to the element and the drive signal controller adjusts thedriving signal so as to maintain the phase shift at substantially apredetermined value.
 3. A control apparatus as claimed in claim 1characterized in that the sensing element is coupled to a drive elementvia a liquid coupling.
 4. A control apparatus as claimed in claim 3,characterized in that the drive element is a piezo-electric element. 5.A control apparatus as claimed in claim 1, characterized in that thesensing element is driven via one of alternating magnetic fields,alternating electrostatic fields, pressure waves and pulsed heating. 6.A control apparatus as claimed in claim 2, in which the predeterminedphase shift is substantially 90 degrees.
 7. A control apparatus asclaimed in claim 2, in which the phase shift is measured by a phasesensitive detector, and the output of the detector is provided to acontroller which controller causes a change to the frequency of thedriving signal.
 8. A control apparatus as claimed in claim 1, furthercomprising at least one other feedback loop for controlling a propertyof the drive signal used to stimulate the sensing element.
 9. A controlapparatus as claimed in claim 8, characterized in that one furtherfeedback loop is provided, and said one further feedback loop controlsthe magnitude of the drive signal.
 10. A control apparatus as claimed inclaim 8, characterized in that a signal from the sensor is phase shiftedand amplified, said amplification being a function of the amplitude ofsaid signal from the sensor, and combined with the drive signal.
 11. Acontrol apparatus as claimed in claim 8, characterized in that anamplitude of the drive signal is modulated as a function of theamplitude of the sensor signal.
 12. An apparatus as claimed in claim 8,characterized in that the or one of the further feedback loops forms afeedback loop synthesising an effective quality factor for the sensingelement in excess of its actual quality factor.
 13. A scanning probemicroscope including a control apparatus as claimed in claim
 1. 14. Achemical or bio-chemical sensor comprising a resonating sensing elementhaving a receptor therein, where the receptor interacts with a substanceunder test, in combination with a control apparatus as claimed inclaim
 1. 15. A sensor as claimed in claim 14, wherein one side of thesensor is coated with a substance sensitive to a target substance undertest.